Answer:
q=quarters, d=dimes
q+d=8
.25q+.1d=1.25
Let's set the first equation to equal d.
d=8-q
.25q+.1(8-q)=1.25
Distribute.
.25q+.8-.1q=1.25
Combine Like Terms
.15q+.8=1.25
Subtract .8
.15q=.45
Divide by .15
q=3
Now, let's solve for d in the first equation.
d+3=8
Subtract 3, and you get d=5
So, there are 5 dimes and 3 quarters in Maribel's pocket.
Check: .25(3)+.1(5)=1.25
.75+.5=1.25
1.25=1.25 which is true.
Pls mark me as brainliest!Jordan has 3 quarters and 5 dimes in his pocket that total to $1.25.
Explanation:Let's assume Jordan has x number of quarters and 8 - x number of dimes in his pocket.
Each quarter is worth 25 cents, so the value of the quarters is 25x cents.
Each dime is worth 10 cents, so the value of the dimes is 10(8-x) cents.
The sum of the values of the quarters and dimes should be equal to $1.25, which is 125 cents. So, we can set up the equation: 25x + 10(8-x) = 125.
Simplifying the equation, we get 25x + 80 - 10x = 125. Combining like terms, 15x + 80 = 125. Subtracting 80 from both sides, 15x = 45. Finally, dividing both sides by 15, we find x = 3.
Therefore, Jordan has 3 quarters and 8 - 3 = 5 dimes in his pocket.
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d-(-3)=12
what is d- negative3=12
Answer:
d=9
Step-by-step explanation:
d-1(-3)=12
d+3=12
subsctract 3 both sides
12-3=9
d = 9
If the line through the points (1,2) and (1,a) is parallel to 6x+2y=-2, what is the value of a?
Two lines are parallel if their slopes are equal. To find the slope of the line through the points (1,2) and (1,a), we can use the formula:
(y2 - y1) / (x2 - x1) = (a - 2) / (1 - 1) = a - 2
To find the slope of the line 6x + 2y = -2, we can rewrite it in slope-intercept form (y = mx + b) by isolating y:
2y = -6x - 2
y = -3x - 1
So the slope of this line is -3.
Since the line through the points (1,2) and (1,a) is parallel to 6x + 2y = -2, we know that the slopes must be equal. Therefore:
a - 2 = -3
Solving for a:
a = -1
So the value of a is -1.
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Alec's parents give him x dollars per month for his allowance. However, since his birthday is
in February, he gets an extra 20% bonus that month.
Pick all the expressions that represent how much Alec's allowance is in February.
x + 0.2x
+
1.2x
*
D
X
⠀
Alec's parents give him x dollars per month for his allowance. However, since his birthday is in February, he gets an extra 20% bonus that month. The allowance in February can be represented by the expression x + 0.2x because Alec will get the regular allowance of x dollars plus an extra 20% bonus which is equal to 0.2x dollars.
x + 0.2x = Alec's allowance in February
The expression 1.2x is not correct because it represents Alec's allowance multiplied by 1.2 which is not the same as the allowance plus the bonus.
So the correct answer is x + 0.2x.
Find the distance between the two points (5, -4) and (3 , 6). Give an exact answer in terms of a square root.
Answer:
√104.
Step-by-step explanation:
To find the distance between two points (x1, y1) and (x2, y2) in a coordinate plane, we can use the distance formula:
d = √((x2 - x1)² + (y2 - y1)²)
So, for the given points (5, -4) and (3, 6), the distance is:
d = √((3 - 5)² + (6 - (-4))²)
d = √((-2)² + (10)²)
d = √(4 + 100)
d = √104
Therefore, the distance between the two points (5, -4) and (3, 6) is √104.
The Karson Transport Company currently has net operating income of 503,000 and pays interest expense of 191,000 . The company plans to borrow 1.15 million on which the firm will pay 11 percent interest. The borrowed money will be used to finance an investment that is expected to increase the firm's net operating income by 408,000 a year.
a) Before the loan is taken out and the investment is made, Karson's times' interest earned ratio is 2.63 times.
b) When the loan and the investment are made, the firm's times interest earned ratio will increase from 2.63 times to 2.87 times.
What is the times' interest earned ratio?The times' interest earned ratio is the ratio that measures the company's ability to meet debt obligations using its net operating income.
The interest earned ratio is computed as the quotient of the net operating income (earnings before interest and taxes) and the interest expense.
Current net operating income = $503,000
Interest expense = $191,000
Times interest earned = 2.63 times ($503,000/$191,000)
Proposed loan = $1.15 million
Interest rate = 11%
Interest amount = $126,500 ($1,150,000 x 11%)
Additional net operating income = $408,000
New net operating income = $911,000 ($503,000 + $408,000)
New interest expense = $317,500 ($191,000 + $126,500)
Adjusted Times interest earned = 2.87 times ($911,000/$317,500)
Thus, if Karson takes the additional loan to finance the investment, its times' interest-earned ratio will increase, showing that it has the ability to settle the debt obligations.
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Question Completion:a. What is Karson's times' interest earned ratio before the loan is taken out and the investment is made?
b. What effect will the loan and the investment have on the firm's times interest earned ratio?
Tiana needs to wrap 2 gifts with no overlap. The boxes are shaped as right rectangular prisms. The length of each box is 22.2 in, the width is 4.8 in, and the height is 14 in. How much wrapping paper does Tiana need to buy? Round to the nearest hundredth. Leave out units.
Answer: Tiana needs to buy 560.64 in. of wrapping paper
Step-by-step explanation: Long sides:
length times width=area
22.2*4.8=106.56
times the number of similar sides
106.56*4=426.24
Short sides:
height times width=area
4.8*14=67.2
times the number of similar sides
67.2*2=134.4
add seperate areas
426.24+134.4=560.64
round to nearest hundredth
560.64 stays the same because there is no thousandth place
A package of 5 pairs of insulated gloves costs $26.95. What is the unit price of the pairs of gloves?
Answer:
$5.93
Step-by-step explanation:
26.95/5=5.93
A data set of monthly expenditures (rounded to the nearest dollar) incurred at coffee shops by a sample of 500
households has a minimum value of $14 and a maximum value of $246. Suppose we want to group these data
into six classes of equal widths.
Assuming we take the lower limit of the first class as $1 and the upper limit of the sixth class as $246,
determine the class limits, boundaries, and midpoints for a grouped quantitative data table.
Hint: To determine the class width, divide upper limit of the sixth class (246) by the number of classes (6).
Therefore , the solution of the given problem of function comes out to be $3,556 this is the total startup expense.
What is meant by the word function?A science called mathematics studies numbers, its variations, arithmetic and the local tissue, shapes, and both their existing and projected limit. The relationship between a group of inputs, which each have a corresponding upper bound, is described by a function. A function is a collection of inputs that together produce a single, recognizable output with each input.
Here,
Because the launch expense exceeds $50,000, any startup expenses that cannot be deducted may be prorated over a 180-month period beginning with the start of business.
The startup costs are divided by the entire number of months authorized for amortization, and the result is then calculated by the number of months that were traded throughout the year.
The Root bark Corporation has been conducting business in the case at hand for 10 months, from March to December 2019.
Amount that can be amortized: ($64,000 / 180 months) * 10 months.
=> $3,556 this is the total startup expense that may be deducted.
Therefore , the solution of the given problem of function comes out to be $3,556 this is the total startup expense.
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Prove the Riemann Hypothesis
Answer:
The Riemann Hypothesis is a conjecture made by mathematician Bernhard Riemann in 1859 that states that all non-trivial zeroes of the Riemann zeta function, which is a complex function that encodes the distribution of prime numbers, lie on the critical line of 1/2. The conjecture is considered one of the most important unsolved problems in mathematics and has yet to be proven or disproven.
There have been many efforts to prove the Riemann Hypothesis over the years, but so far, no one has been able to provide a definitive proof. Many mathematicians have made significant progress in understanding the conjecture and its implications, but a proof remains elusive.
Some of the notable efforts to prove the Riemann Hypothesis include:
In 1859, Riemann himself provided evidence to support the conjecture by showing that the first few non-trivial zeroes lie on the critical line.
In 1911, the mathematician G.H. Hardy proved that an infinite number of non-trivial zeroes lie on the critical line.
In the 1970s, the mathematician A. Selberg proved that an infinite number of non-trivial zeroes lie in the critical strip, which is a slightly wider region around the critical line.
Despite these advances, a proof of the Riemann Hypothesis remains elusive and it continues to be one of the most important unsolved problems in mathematics. Some of the most recent and notable progress on the Riemann Hypothesis has been made by researchers using computational methods such as the Turing method and the Gram-Schmidt orthogonalization method, but the proof is not yet proven.
It's worth mentioning that the Riemann Hypothesis is considered an important problem in mathematics, and solving it could have far-reaching implications for many areas of mathematics and physics, including number theory, cryptography and prime number distribution.
Step-by-step explanation:
Solve for w.
5w+3=-7
Answer:
w = -2
Step-by-step explanation:
5w+3=-7
minus 3 from both sides:
5w=-10 then divide both sides by 5 to go get w by it self
w=-2
The value of w is -2.
What is an Equation?An equation is the statement of two expressions located on two sides connected with an equal to sign. The two sides of an equation is usually called as left hand side and right hand side.
Given is an equation with 1 variable w.
5w + 3 = -7
We have to find the value of w.
We need to get the variable w on the left hand side and a number on the right hand side of the given equation.
Subtracting both sides of the equation by -3,
5w + 3 - 3 = -7 - 3
5w = -10
Dividing both sides of the equation by 5,
5w/5 = -10/5
w = -2
Hence we get the value of w as -2.
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at a factory that produces pistons for cars machine 1 produce 648 satisfactory pistons and 162 and satisfactory Pistons today machine two produced 560 and satisfactory Pistons and 140 unsatisfactory pistons today. Suppose that one piston from machine 1 and one piston from machine 2 are chosen at random from today's batch. what is the probability that the piston chosen from machine 1is satisfactory and the piston chosen from machine 2 is unsatisfactory?
b Write a description of the circuit diagram below.
A4
L
A₁
A3
A₂
Answer:
the circuit a1 and a3 are parallel to each other
rest of them must be in series
A table of values of a linear function is shown below.
y
slope:
y-intercept:
equation:
Find the slope and y-intercept of the function's graph, and find the equation for the function.
Answer:
The slope is -1
The y-intercept is -8
The equation is y = -x -8
Step-by-step explanation:
The slope is the change in y over the change in x. As the y is decreasing by 1. The x is increasing by 1
-1/1 = -1
The slope is -1.
The y-intercept is the y value when the x value is 0. When x = 0, y = -8
The y-intercept is -8.
y = mx + b
y = -1x - 8 I don't nee the 1 so I am going to write it without it.
y = -x - 8
An electrical parts manufacturing company produces resistors of
resistance 700 ohms and they quarantee that the variations will
stay within a range of +5%. Which equation can be used to find
the lowest and highest resistance that can be achieved?
x+700=5
x+700=35
Ix-700=5
x-7001=35
Answer:
d. x-700=35
Step-by-step explanation:
The statement says that the variations will stay within a range of +5%, so the resistance can be increased by 5% of 700 ohms. To find the highest resistance that can be achieved, you can use the formula:
x = 700 + (700 * 5%) = 700 + 35 = 735 ohms
To find the lowest resistance that can be achieved, you can subtract the same percentage (5%) of 700 ohms:
x = 700 - (700 * 5%) = 700 - 35 = 665 ohms
So the lowest and highest resistance that can be achieved are 665 ohms and 735 ohms respectively.
2 irrational numbers that add up to 2
Answer:
An example of two irrational numbers that add up to 2 are √2 and √2 - 2.
√2 is an irrational number as it cannot be expressed as a ratio of two integers.
√2 - 2 is also an irrational number as it is the difference of two irrational numbers.
Both √2 and √2 - 2 are irrational numbers and √2 + (√2 - 2) = √2 + √2 - 2 = 2
So, √2 and √2 - 2 are two irrational numbers that add up to 2.
There is a line that includes the point (0, -20) and has a slope of 1. What is its equation in
slope-intercept form?
Write your answer using integers, proper fractions, and improper fractions in simplest form.
PLEASE HELPP!!
The line that includes the point (0, -20) and has a slope of 1 will be y = x - 20.
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
The line has a slope of 1. Then the equation of the line is given as,
y = x + c
There is a line that includes the point (0, -20). Then the equation of the line is given as,
- 20 = 0 + c
c = - 20
Then the equation of the line is y = x - 20.
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Three softball players discussed their batting averages after a game.
................Probability
Player 1: four sevenths
Player 2: five eighths
Player 3: three sixths
By comparing the probabilities and interpreting the likelihood, which statement is true?
A. Player 1 is more likely to hit the ball than Player 2 because P(Player 1) > P(Player 2)
B. Player 2 is more likely to hit the ball than Player 1 because P(Player 2) > P(Player 1)
C. Player 3 is more likely to hit the ball than Player 1 because P(Player 3) > P(Player 1)
D. Player 3 is more likely to hit the ball than Player 2 because P(Player 3) > P(Player 2)
Answer:
B. Player 2 is more likely to hit the ball than Player 1 because P(Player 2) > P(Player 1)
Step-by-step explanation:
This statement is true because the probability of Player 2, which is five eighths, is greater than the probability of Player 1, which is four sevenths. It is important to note that in order to compare the probabilities, it is necessary to convert the fractions to a common denominator. In this case, the common denominator is 56, then we can say that P(Player 2) = 35/56 and P(Player 1) = 28/56. Since 35/56 > 28/56, it is more likely that Player 2 will hit the ball than player 1.
Answer: B: Player 2 is more likely to hit the ball than Player 1 because P(Player 2) > P(Player 1)
Step-by-step explanation:
Each backpack in the store is on sale for five dollars of the original price how much does this affect the mean median and mode of prices
The sale reduces the original price of the backpack, this reduces the mean, median and mode of the prices.
What is mean, median and mode?The measurements of central tendency are the mean, median, and mode. The means of a group of numbers is their average. The value that is in the middle of a group of numbers is known as the median. The number that appears most frequently out of a group of numbers is called the mode.
In a scale all the items are at a discounted rate this decreases the prices of the commodity thus decreasing the mean, median and mode of the prices.
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Which point is a solution to the system of linear equations? y = −x + 3 x − 3y = 15? (−1, 5) (0, 3) (3, 0) (6, −3)
( 3, 0 ) is a solution to the system of linear equations .
What is a linear equation explain?
An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.
Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables. When an algebraic equation is graphed, a linear equation always produces a straight line since each term has an exponent of 1.
y = −x + 3
( 3, 0 ) Put in equation
0 = - 3 + 3
0 = 0
− 3y = 15
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Last time it said 14 was wrong, is 14.1 correct?
Quadrilateral GHIJ is similar to quadrilateral KLMN find the measure of side MN
Answer: I believe 14.1 should be correct
Step-by-step explanation:
Given that we know one side length is 52 and the other is 21, we can use these values to create a scale.
52/21 = 2.4761, so we know that all sides will decrease by a scale of this value.
Given that, we can find the length of the MN. 35/2.4761 = 14.135
The question asks to round to the nearest tenth, so the answer should be 14.1. hope this helps!
Pls help me with this one
An equation for a rational function with the given characteristics is f(x)=3/2 (x+3)(x-3)/(x+2)(x-2)
What is a function?A relation is a function if it has only One y-value for each x-value.
Since there are vertical asymptotes at X = -2 and X = 2, the denominator will have the terms (x+2) and (x-2)
Since the x intercepts are -3 and 3, the numerator will have the terms (x+3) and (x-3)
So far we have f(X) = a(x+3)(x-3)/(x+2)(x-2)
o find the value of A, we look at the horizontal asymptote. The horizontal asymptote describes what the function looks like when x approaches infinity, therefore a = 3/2
f(x)=3/2 (x+3)(x-3)/(x+2)(x-2)
Hence, an equation for a rational function with the given characteristics is f(x)=3/2 (x+3)(x-3)/(x+2)(x-2)
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in 2000 the population of Africa was 807million and by 2011 it had grown to 1052million.find the exponential growth function that models the data
Study finds that Africa’s population increased by over 1 billion, from 228.7 million in 1950 to 1.341 billion in 2020: 431 million in Eastern Africa; 404 million in Western Africa; 247.5 million in Northern Africa; 193.5 million in Middle Africa; and 64.5 million in Southern Africa.
Exponential Decay APPLICATION The half-life of strontium-90 is 28 years, meaning that after 28 years a given amount of the substance will have decayed to half the original amount. Application In 2000, the population of Africa was 807 million and by 2011 it had grown to 1052 million. Use the exponential growth model in which t is the number of years after 2000, to find the exponential growth function that models the data. The model isApplication continued:- By which year will Africa’s population reach 2,000 million. Use the exponential growth function model: to find how long it will take to reach a population of 2,000 million.
Nigeria is forecast to become the world’s third-biggest country – after India and China – with 405 million people. The main reason for these demographic trends is Africa’s high fertility rate compared with other regions
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The lengths of the legs of a right triangle are 7 in. and 2 in.
What is the length of the hypotenuse?
Enter your answer rounded to the nearest tenth
Answer: To find the length of the hypotenuse of a right triangle, we can use the Pythagorean theorem, which states that the square of the length of the hypotenuse of a right triangle is equal to the sum of the squares of the lengths of the other two sides. The theorem is written as c² = a² + b², where c is the length of the hypotenuse and a and b are the lengths of the other two sides.
In this problem, we are given that the lengths of the legs of the right triangle are 7 inches and 2 inches. We can substitute these values into the Pythagorean theorem and solve for c, the length of the hypotenuse.
So, we have c² = 7² + 2².
So, c² = 49 + 4
So, c² = 53
Now, we can take the square root of both sides of the equation, since c² = 53, we can say c = √53
To round to the nearest tenth, we look at the digit in the thousandths place (the 3rd digit after the decimal point). Since 3 is greater than or equal to 5, we round up, so c = 7.28, so the hypotenuse is 7.28 inches.
Step-by-step explanation:
Answer:10
Step-by-step explanation: round it together and you get 10
